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Cover Photo 2007-2008 Catalog Online

Course Descriptions:






 

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Mathematics (MTH)

Chairperson: Professor Pakula

010 Basic Math (3)

Real numbers; operation with fractions and decimals. Proportions and related problems. Basic algebra: solving first-degree equations and systems of equations. Applications. (Lec. 3) S/U only. Credits may not be used toward the minimum credits required for graduation or for general education.

099 Basic Algebra and Trigonometry (3)

Review of basic algebra and trigonometry: operations of real numbers and algebraic expressions, negative and fractional exponents, polynomials and fractional expressions, equations and systems of equations, inequalities, right triangle trigonometry and applications. (Lec. 3) For students not sufficiently prepared to take other mathematics courses. Credits may not be used toward the minimum credits required for graduation or for general education. S/U only.

107 Introduction to Finite Mathematics (3)

Concepts and processes of modern mathematics concerned with sets, the theory of probability, and statistics. Role of these concepts in today’s social and physical sciences. (Lec. 3) Pre: passing a placement test. Not open to mathematics majors. (MQ)

108 Topics in Mathematics (3)

Introduces the nonmathematics student to the spirit of mathematics and its applications. Presupposes no mathematical background beyond University admission requirements. Emphasis is on development of reasoning ability as well as manipulative techniques. (Lec. 3) Pre: passing a placement test. Not open to mathematics majors. (MQ)

109 Politics and Mathematics

See Political Science 109. (MQ)

110 Mathematical Foundations for Business Analysis (3)

Equations of first and second degree. Inequalities. Exponential and logarithmic functions. Emphasis on business applications. Introduction to linear algebra and matrices. Introduction to spreadsheets. Designed for students who want to strengthen their background in math before BAC 120. (Lec. 3). Not for credit for mathematics majors and not for general education credit.

111 Precalculus (3)

Equations of first and second degree, systems of equations. Inequalities. Functions and graphs. Exponential, logarithmic, and trigonometric functions. Applications. Introduction to analytic geometry. Complex numbers. Designed for students who need to strengthen their background in mathematics below calculus. (Lec. 3) Pre: passing a placement test. Not for credit for mathematics majors. (MQ)

131 Applied Calculus I (3)

Basic topics in calculus for students who do not need all the topics in 141. Limits, derivatives, and integrals of algebraic, logarithmic, and exponential functions. Applications including graphing, maxima and minima problems, etc. (Lec. 3) Pre: passing a placement test. Not for major credit in mathematics. Not open to students with credit or concurrent enrollment in 141. (MQ)

132 Applied Calculus II (3)

Continuation of 131. Topics related to trigonometric functions, integration by parts and partial fractions, partial derivatives, infinite series. Applications to problems such as optimization, probability theory, simple differential equations. (Lec. 3) Pre: 131 or 141 or permission of chairperson. Not for major credit in mathematics. Not open to students with credit or concurrent enrollment in 142.

141 Introductory Calculus with Analytic Geometry (4)

Topics in analytic geometry, functions and their graphs, limits, the derivative, applications to finding rates of change and extrema and to graphing, the integral, and applications. (Lec. 3, Rec. 1) Completion of four units of high school mathematics, including trigonometry, recommended. Pre: passing a placement test. Not open to students with credit or concurrent enrollment in 131. (MQ)

142 Intermediate Calculus with Analytic Geometry (4)

Continues the study of calculus for the elementary algebraic and transcendental functions of one variable. Topics include the technique of integration, improper integrals, indeterminate forms, and calculus using polar coordinates. (Lec. 3, Rec. 1) Pre: 141 or permission of chairperson. Not open to students with credit or concurrent enrollment in 132.

208 Mathematics for Elementary School Teachers (3)

Selected topics in mathematics central to the elementary school curriculum, including problem solving, number systems, functions and relations, probability and statistics, and geometry. (Lec. 3) Pre: admission to elementary education program and prior completion of general education mathematics requirement. Not open to mathematics majors or mathematics education majors.

215 Introduction to Linear Algebra (3)

Detailed study of finite dimensional vector spaces, linear transformations, matrices, determinants, and systems of linear equations. (Lec. 3) Pre: 131, 141, or equivalent.

243 Calculus for Functions of Several Variables (3)

Topics include coordinates for space, vector geometry, partial derivatives, directional derivatives, extrema, Lagrange multipliers, and multiple integrals. (Lec. 3) Pre: 142.

244 Differential Equations (3)

Classification and solution of differential equations involving one independent variable. Applications to the physical sciences. Basic for further study in applied mathematics and for advanced work in physics and engineering. (Lec. 3) Pre: 243.

307 Introduction to Mathematical Rigor (3)

Introduction to the language of rigorous mathematics: logic, set theory, functions and relations, cardinality, induction, methods of proof. Emphasis on precise written and oral presentation of mathematical arguments. (Lec. 3) Pre: 141.

316 Algebra (3)

Theory and structure of groups. Topics from ring theory, principal ideal domains, unique factorization domains, polynomial rings, field extensions, and Galois theory. (Lec. 3) Pre: 215 and 307.

322 Concepts of Geometry (3)

Survey of geometrical systems including non-Euclidean, affine, and projective spaces and finite geometries. A modern view of Euclidean geometry using both synthetic and analytic methods. (Lec. 3) Pre: 215 or permission of instructor.

362 Advanced Engineering Mathematics I (3)

Algebra of complex numbers, matrices, determinants, quadratic forms. Linear differential equations with constant coefficients. Partial differential equations. (Lec. 3) Pre: 142. Not for major credit in mathematics.

363 Advanced Engineering Mathematics II (3)

Laplace and Fourier transforms. Analytic functions. Cauchy’s theorem and integral formula. Power series in the complex domain. Laplace and Fourier inverse integrals. Introduction to probability. (Lec. 3) Pre: 362 or equivalent. Not for major credit in mathematics.

381 History of Mathematics (3)

General survey course in development and philosophy of mathematics. Provides a cultural background and foundation for advanced study in various branches of the subject. (Lec. 3) Pre: 142 or equivalent.

382 Number Theory (3)

Some of the arithmetic properties of the integers including number theoretic functions, congruences, diophantine equations, quadratic residues, and classically important problems. (Lec. 3) Pre: 141 or permission of instructor.

391 Special Problems (1-3)

Advanced work under the supervision of a faculty member and arranged to suit the individual requirements of the student. (Independent Study) Pre: permission of chairperson.

393 Undergraduate Seminar (1)

Preparation and presentation of selected topics in oral and written form. (Seminar) Pre: permission of chairperson.

418 Matrix Analysis (3)

Canonical forms, functions of matrices, characteristic roots, applications to problems in physics and engineering. (Lec. 3) Pre: 215 or 362 or permission of instructor.

420 Re-examining Mathematical Foundations for Teachers (3)

Connects ideas covered in upper level math courses to topics taught in secondary school. Designed for teachers. (Lec. 3) Pre: 316 or permission.

425 Topology (3)

Abstract topological spaces and continuous functions. Generalizations of some classical theorems of analysis. (Lec. 3) Pre: 243 and 307, or permission of instructor or chairperson.

435 Introduction to Mathematical Analysis I (3)

Sets and functions, real topology, continuity and uniform continuity, derivatives, the Riemann integral, improper integrals. Detailed proofs emphasized. (Lec. 3) Pre: 243; 307 is strongly recommended.

436 Introduction to Mathematical Analysis II (3)

Sequences and series of functions, implicit and inverse function theorems, topology of Euclidean space, transformation of multiple integrals. Detailed proofs emphasized. (Lec. 3) Pre: 435.

437, 438 Advanced Calculus and Application I, II (3 each)

Sequences, limits, continuity, differentiability, Riemann integrals, functions of several variables, multiple integrals, space curves, line integrals, surface integrals, Green’s theorem, Stokes’ theorem, series, improper integrals, uniform convergence, Fourier series, Laplace transforms. Applications to physics and engineering emphasized. (Lec. 3) Pre: (for 437) 243 and credit or concurrent enrollment in 215 or 362. Pre: (for 438) 437.

441 Introduction to Partial Differential Equations (3)

One-dimensional wave equation. Linear second order partial differential equations in two variables. Separation of variables and Fourier series. Nonhomogeneous boundary value problems. Green’s functions. (Lec. 3) Pre: 244 or 442.

442 Introduction to Difference Equations (3)

Introduction to linear and nonlinear difference equations; basic theory, z-transforms, stability analysis, and applications. (Lec. 3) Pre: 243.

444 Ordinary Differential Equations (3)

Introduction to fundamental theory of ordinary and functional-differential equations. Series and numerical methods. Topics from stability, periodic solutions, or boundary-value problems. Applications to physics, engineering, biology. (Lec. 3) Pre: 244 or 362 or 442.

447 (or CSC 447) Discrete Mathematical Structures (3)

Concepts and techniques in discrete mathematics. Finite and infinite sets, graphs, techniques of counting, Boolean algebra and applied logic, recursion equations. (Lec. 3) Pre: junior standing or better in physical or mathematical sciences, or in engineering, or permission of instructor.

451 Introduction to Probability and Statistics (3)

Theoretical basis and fundamental tools of probability and statistics. Probability spaces, properties of probability, distributions, expectations, some common distributions, and elementary limit theorems. (Lec. 3) Pre: 243 or equivalent.

452 Mathematical Statistics (3)

Continuation of 451 in the direction of statistics. Basic principles of statistical testing and estimation, linear regression and correlation. (Lec. 3) Pre: 451.

456 Introduction to Random Processes (3)

Conditional probability and expectation. Mean and covariance functions. Calculus of random processes. Introduction to Gaussian processes, Poisson processes, stationary processes, and Markov chains with applications. (Lec. 3) Pre: 451 or equivalent.

461 Methods of Applied Mathematics (3)

Topics selected from vector analysis, elementary complex analysis, Fourier series, Laplace transforms, special functions, elementary partial differential equations. Emphasis on development of techniques rather than mathematical theory. (Lec. 3) Pre: 244 or 362 or 442.

462 Functions of a Complex Variable (3)

First course in the theory of functions of a single complex variable, including analytic functions, power series, residues and poles, complex integration, conformal mapping, and applications. (Lec. 3) Pre: 243 or equivalent.

464 Advanced Engineering Mathematics III (3)

Topics from Fourier series and integrals. Partial differential equations and boundary value problems. Bessel functions and Legendre polynomials. Conformal mappings. (Lec. 3) Pre: 362 and 363 or permission of instructor. Not for graduate credit in mathematics.

471 Introduction to Numerical Analysis I (3)

Interpolation, solution of nonlinear equations, numerical evaluation of integrals, special topics. (Lec. 3) Pre: 243, CSC 201 or equivalent, or permission of instructor.

472 Introduction to Numerical Analysis II (3)

Numerical solution of ordinary differential equations, systems of linear equations, least squares, approximation, special topics. (Lec. 3) Pre: 243, CSC 201 or equivalent, or permission of instructor.

492 Special Problems (1-3)

Advanced work under the supervision of a faculty member arranged to suit the individual requirements of the student. (Independent Study) Pre: permission of chairperson.

513 Linear Algebra (3)

Linear spaces and transformations, linear functionals, adjoints, projections, diagonalization, Jordan form of matrices, inner products; positive, normal, self-adjoint, and unitary operators; spectral theorem, bilinear and quadratic forms. (Lec. 3)

515, 516 Algebra I, II (3 each)

Groups, rings, modules, commutative algebra. (Lec. 3) Pre: 316. In alternate years.

525 Topology (3)

Topological spaces, separation properties, connectedness, compactness, uniformities. Function spaces, spaces of continuous functions, and complete spaces. (Lec. 3) Pre: 425 or equivalent. In alternate years.

535, 536 Measure Theory and Integration (3 each)

Elements of topology and linear analysis. Lebesgue measure and integration in R, in Rn, and in abstract spaces. Convergence theorems. Bounded variation, absolute continuity, and differentiation. Lebesgue-Stieltjes integral. Fubini and Tonelli theorems. The classical Banach spaces. (Lec. 3) Pre: 435.

545, 546 Ordinary Differential Equations I, II (3 each)

Existence and uniqueness theorems. Continuous dependence on parameters and initial conditions. Singularities of the first and second kinds, self-adjoint eigenvalue problems on a finite interval. Oscillation and comparison theorems. Introduction to delay and difference equations. Elements of stability theory of Lyapunov’s second method. (Lec. 3) Pre: 435. In alternate years.

547 (or CSC 547) Combinatorics and Graph Theory (3)

Enumeration: generating functions, recurrence relations, classical counting numbers, inclusion-exclusion, combinatorial designs. Graphs and their applications: Euler tours, Hamilton cycles, matchings and coverings in bipartite graphs, the four-color problem. (Lec. 3) Pre: 215 or equivalent. In alternate years.

548 (or CSC 548) Topics in Combinatorics (3)

Topics such as Ramsey theory, Polya theory, network flows and the max-flow-mincut variations, applications in operations research; finite fields and algebraic methods; block designs, coding theory, other topics. (Lec. 3) Pre: 547 or permission of instructor. In alternate years.

550 Probability and Stochastic Processes (3)

Review of probability theory. Generating functions, renewal theory, Markov chains and processes, Brownian motions, stationary processes. (Lec. 3) Pre: 437 or 435 and 451, or permission of instructor. In alternate years.

551 Mathematical Statistics (3)

Theory of estimation and hypothesis testing. Large sample methods. Regression and analysis of variance. (Lec. 3) Pre: 437 or 435 and 451, or permission of instructor. In alternate years.

561 Advanced Applied Mathematics (3)

Linear spaces, theory of operators. Green’s functions, eigenvalue problems of ordinary differential equations. Application to partial differential equations. (Lec. 3)

562 Complex Function Theory (3)

Rigorous development of theory of functions. Topology of plane, complex integration, singularities, conformal mapping. (Lec. 3) Pre: 435 and 436 or 437 and 438 and permission of instructor. In alternate years.

572 Numerical Analysis (3)

Further numerical methods of solution of simultaneous equations, partial differential equations, integral equations. Error analysis. (Lec. 3)

575 Approximation Theory and Applications to Signal Processing

See Electrical Engineering 575.

591, 592 Special Problems (1-3 each)

Advanced work under the supervision of a member of the department arranged to suit the individual requirements of the student. (Independent Study) Pre: permission of chairperson.

599 Master’s Thesis Research

Number of credits is determined each semester in consultation with the major professor or program committee. (Independent Study) S/U credit.

629, 630 Functional Analysis I, II (3 each)

Banach and Hilbert spaces, basic theory. Bounded linear operators, spectral theory. Applications to analysis. Application to a special topic such as differential operators, semigroups and abstract differential equations, theory of distributions, or ergodic theory. (Lec. 3) Pre: 536 or permission of instructor.

641 Partial Differential Equations I (3)

First order systems. The Cauchy-Kowalewsky theorem. The Cauchy problem. Classification of partial differential equations. Hyperbolic equations. Mainly the theory of the subject. Students interested in techniques for the solution of standard equations should take 441. (Lec. 3) Pre: 215, 435, and 462. In alternate years.

642 Partial Differential Equations II (3)

Elements of potential theory. Elliptic equations. Green’s function. Parabolic equations. Introduction to the theory of distributions. (Lec. 3) Pre: 641. In alternate years.

691, 692 Special Topics I, II (3 each)

Advanced topics of current research in mathematics will be presented with a view to expose the students to the frontiers of the subject. (Independent Study) Pre: permission of chairperson.

699 Doctoral Dissertation Research

Number of credits is determined each semester in consultation with the major professor or program committee. (Independent Study) S/U credit.

930 Workshop in Mathematics Topics for Teachers (0-3)

Especially designed for teachers of mathematics. Basic topics of mathematics from an advanced or pedagogical perspective. (Workshop) Pre: teacher certification. Not for degree credit.


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